2022/01/10 by Ruodu Wang, Zhenyuan Zhang, Wang, Ruodu +1
Mathematics · #FOS: Economics and business #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2201.03483
openalex publication_date 2022/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous optimal transport (SOT). The new framework is motivated by the need to transport resources of different types simultaneously, i.e., in single trips, from specified origins to destinations; similarly, in economic matching, one needs to couple two groups, e.g., buyers and sellers, by equating supplies and demands of different goods at the same time. The mathematical structure of simultaneous transport is very different from the classic setting of optimal transport, leading to many new challenges. The Monge and Kantorovich formulations are contrasted and connected. Existence conditions and duality formulas are established. More interestingly, by connecting SOT to a natural relaxation of martingale optimal transport (MOT), we introduce the MOT-SOT parity, which allows for explicit solutions of SOT in many interesting cases.